2.4: Frequency Tables and Line Plots
Introduction
Working in the Garden
As summer passes, the vegetables in Tania and Alex’s vegetable garden have been growing nicely. In fact, they have so many vegetables that they don’t know how they are going to have enough time to work on everything that needs to be done.
Because having a garden is more work than they imagined, Tania and Alex have asked some of their friends to help them in the garden. Alex read an article in the newspaper about CSA’s, community supported agriculture. This is when people work on a farm and get some of the vegetables in exchange for their efforts. Tania and Alex have decided to do the same thing. They have offered their friends vegetables in exchange for their work.
Now instead of two people working in the garden, they have seven. To be sure that everything gets done, they decide to keep track of how many people they have working in the garden each day. For two weeks, Alex and Tania keep track of how many people are working in the garden on each day. Here are their results.
2, 4, 5, 6, 1, 2, 3, 4, 5, 6, 6, 7, 1, 2
To get everything done in the garden, Tania and Alex know that at least three people need to be working on each day. When they look at the information they can see that this is not always the case.
Tania wants to organize the information so that she can share it with the group.
Tania isn’t sure how to build a table and plot the information out on a line plot so that everyone can see the statistics.
How can she show the frequency of people working in the garden?
In this lesson, you will learn about frequency tables and line plots. Both of these skills will help Tania to display her data so that everyone can read it easily.
What You Will Learn
In this lesson you will learn how to:
- Make a frequency table to organize and display given data.
- Make a line plot given a frequency table.
- Make a frequency table and line plot given unorganized data.
- Collect, organize, display and analyze real-world data using frequency tables and line plots
Teaching Time
I. Make a Frequency Table to Organize and Display Given Data
What is data?
Data is information, usually numbers, connected with real life situations. If we were going to count how many people came to an amusement park in one day, the number of people that we counted would be the data.
What does it mean when we organize data?
Organizing data means organizing numbers taken from real world information. For instance, if we use the example above, we would be taking the counts of the number of people who visited the amusement park and writing them in a way that is easy to read.
There are lots of different ways to organize data so that it is easy to read.
One way of organizing data is to use a frequency table.
A frequency table is a table that shows how often something occurs.
First, we count or keep track of information, then we take that information and put it into a table with different columns.
Let’s look at an example.
Example
John counted the number of people who were in the shoe store at the same time, in one day. Here are his results:
1, 1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8
We call this data organized data because it is in numerical order and isn’t all mixed up.
When we have information or data like this, we can examine or analyze the data for patterns.
You can see here that the range of people who were in the store was between 1 and 8. No more than eight people were in the shoe store at the same time on this particular day.
We can put this information into a frequency table.
A frequency table is a chart that shows how often something occurs.
For this problem, we will look at the frequency of people entering the store.
To do this, we want to look at how many times one person was in the store, how many times two people were in the store, how many times three people were in the store, etc.
Here is our table.
Notice that it has two columns. Column 1 is named “Number of People Who Were In the Store” and Column 2 is named “Frequency”.
Number of people who were in the store | Frequency |
---|---|
1 | 2 |
2 | 1 |
3 | 1 |
4 | 2 |
5 | 2 |
6 | 2 |
7 | 2 |
8 | 1 |
Whenever we want to see how often something occurs, we can do this by building a frequency table.
Here are few for you to try on your own. Take the following organized data and build a frequency table to display the data.
1. Here is information about the number of dogs counted in the dog park over five days.
4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8
2. Here is the number of children who entered the park throughout the day.
1, 1, 2, 3, 3, 3, 4, 5, 5, 7, 7, 8
Remember to include 6 in your chart even though there weren’t six children who entered the park. You would enter a 0 for the frequency of 6 children.
Take a minute and check your work with a peer.
II. Make a Line Plot Given a Frequency Table
A line plot is another display method we can use to organize data.
Like a frequency table, it shows how many times each number appears in the data set. Instead of putting the information into a table, however, we graph it on a number line. Line plots are especially useful when the data falls over a large range. Take a look at the data and the line plot below.
This data represents the number of students in each class at a local community college.
30, 31, 31, 31, 33, 33, 33, 33, 37, 37, 38, 40, 40, 41, 41, 41
The first thing that we might do is to organize this data into a frequency table. That will let us know how often each number appears.
# of students | Frequency |
---|---|
30 | 1 |
31 | 3 |
32 | 0 |
33 | 4 |
34 | 0 |
35 | 0 |
36 | 0 |
37 | 2 |
38 | 1 |
39 | 0 |
40 | 2 |
41 | 3 |
Now if we look at this data, we can make a couple of conclusions.
- The range of students in each class is from 30 to 41.
- There aren’t any classes with 32, 34, 35, 36 or 39 students in them.
Now that we have a frequency table, we can build a line plot to show this same data.
Building the line plot involves counting the number of students and then plotting the information on a number line. We use \begin{align*}X\end{align*}’s to represent the number of classes that has each number of students in it.
Let’s look at the line plot.
Notice that even if we didn’t have a class with 32 students in it that we had to include that number on the number line. This is very important. Each value in the range of numbers needs to be represented, even if that value is 0.
Let’s use this line plot to answer some questions.
- How many classes have 31 students in them?
- How many classes have 38 students in them?
- How many classes have 33 students in them?
Take a minute to check your answers with a peer.
III. Make a Frequency Table and Line Plot Given Unorganized Data
How can we make a frequency table and line plot when our data is unorganized?
Unorganized data is data that is not written in numerical order.
Another way to think about it is that we can have numbers that are mixed up.
Let’s look at an example.
Example
Jeff counted the number of ducks he saw swimming in the pond each morning on his way to school. Here are his results:
6, 8, 12, 14, 5, 6, 7, 8, 12, 11, 12, 5, 6, 6, 8, 11, 8, 7, 6, 13
Jeff’s data is unorganized. It is not written in numerical order.
When we have unorganized data, the first thing that we need to do is to organize it in numerical order.
6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 11, 11, 12, 12, 12, 13, 14
Next, we can make a frequency table.
There are two columns in the frequency table. The first is the number of ducks and the second is how many times each number of ducks was on the pond. The second column is the frequency of each number of ducks.
Number of Ducks | Frequency |
---|---|
6 | 5 |
7 | 2 |
8 | 4 |
9 | 0 |
10 | 0 |
11 | 2 |
12 | 3 |
13 | 1 |
14 | 1 |
Now that we have a frequency table, the next step is to make a line plot. Then we will have two ways of examining the same data.
Here is a line plot that shows the duck information.
Here are some things that we can observe by looking at both methods of displaying data:
- In both, the range of numbers is shown. There were between 6 and 14 ducks seen, so each number from 6 to 14 is represented.
- There weren’t any days where 9 or 10 ducks were counted, yet both are represented because they fall in the range of ducks counted.
- Both methods help us to visually understand data and its meaning.
Real Life Example Completed
Working in the Garden
Remember Tania and Alex and the garden? Well, now it is time to help Tania to create a frequency table and a display that shows the data she collected about the number of workers in the garden each day.
Let’s look at the problem once more.
As summer passes, the vegetables in Tania and Alex’s vegetable garden have been growing nicely. In fact, they have so many vegetables that they don’t know how they are going to have enough time to work on everything that needs to be done.
Because having a garden is more work than they imagined, Tania and Alex have asked some of their friends to help them in the garden. Alex read an article in the newspaper about CSA’s, community supported agriculture. This is when people work on a farm and get some of the vegetables in exchange for their efforts. Tania and Alex have decided to do the same thing. They have offered their friends vegetables in exchange for their work.
Now instead of two people working in the garden, they have seven. To be sure that everything gets done, they decide to keep track of how many people they have working in the garden each day. For two weeks, Alex and Tania keep track of how many people are working in the garden on each day. Here are their results.
2, 4, 5, 6, 1, 2, 3, 4, 5, 6, 6, 7, 1, 2
To get everything done in the garden, Tania and Alex know that at least three people need to be working on each day. When they look at the information they can see that this is not always the case.
Tania wants to organize the information so that she can share it with the group.
First, we go through and underline all of the important information. This has already been done for you.
Next, you can see that we have unorganized data. Let’s organize the data that Tania and Alex collected so that it is easier to work with.
2, 4, 5, 6, 1, 2, 3, 4, 5, 6, 6, 7, 1, 2
1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 6, 6, 7
Here is the data reorganized numerically.
We can see that the range of numbers is from 1 to 7.
Next, we need to create a frequency table that shows this data.
# of People Working | Frequency |
---|---|
1 | 2 |
2 | 3 |
3 | 1 |
4 | 2 |
5 | 1 |
6 | 3 |
7 | 1 |
Now, let’s draw a line plot to show the data in another way.
Now that we have the visual representations of the data, it is time to draw some conclusions.
Remember that Tania and Alex know that there needs to be at least three people working on any given day.
By analyzing the data, you can see that there are five days when there are only one or two people working.
With the new data, Tania and Alex call a meeting of all of the workers. When they display the data, it is clear why everything isn’t getting done.
Together, they are able to figure out which days need more people, and they solve the problem.
Vocabulary
Here are the vocabulary words that we have used in this lesson.
- Frequency
- how often something occurs
- Data
- information about something or someone-usually in number form
- Analyze
- to look at data and draw conclusions based on patterns or numbers
- Frequency table
- a table or chart that shows how often something occurs
- Line plot
- Data that shows frequency by graphing data over a number line
- Organized data
- Data that is listed in numerical order
Technology Integration
- http://www.hstutorials.net/math/preAlg/php/php_12/php_12_01_x13.htm – Solving a problem using frequency tables and line plots.
- http://www.youtube.com/watch?v=STpxFH7Cpkc – Using frequency tables and line plots.
Time to Practice
Directions: The following frequency table shows data regarding the number of people who attended different movies in one week. Use the following frequency table to answer each question.
# of People at the movies per week | Frequency |
---|---|
20 | 4 |
50 | 3 |
85 | 3 |
90 | 5 |
120 | 2 |
1. If we were to create a list of this data, is the following list correct or incorrect?
20, 20, 20, 20, 50, 50, 50, 90, 90, 90, 85, 85, 85, 120, 120
2. Why?
3. Would you consider the list in number 1 to be organized or unorganized data?
4. Explain the difference.
5. How many showings had 90 people or more in attendance?
6. How many showings had less than 50 people in attendance?
7. How many showings had less than 70 people in attendance?
8. True or false. This data also tells you which showings had the most people in attendance.
9. True or false. There were two showings that had 78 people in attendance.
10. Use the frequency table and draw a line plot of the data.
Directions: Here is a line plot that shows how many seals came into the harbor in La Jolla California during an entire month. Use it to answer the following questions.
11. How many times did thirty seals appear on the beach?
12. Which two categories have the same frequency?
13. How many times were 50 or more seals counted on the beach?
14. True or False. This line plot shows us the number of seals that came on each day of the month.
15. True or False. There weren’t any days that less than 30 seals appeared on the beach.
Directions: Organize each list of data. Then create a frequency table to show the results. There are two answers for each question.
16. 8, 8, 2, 2, 2, 2, 2, 5, 6, 3, 3, 4
17. 20, 18, 18, 19, 19, 19, 17, 17, 17, 17, 17
18. 100, 99, 98, 92, 92, 92, 92, 92, 92, 98, 98
19. 75, 75, 75, 70, 70, 70, 70, 71, 72, 72, 72, 74, 74, 74
20. 1, 1, 1, 1, 2, 2, 2, 3, 3, 5, 5, 5, 5, 5, 5, 5